38.6.52 problem 52 (b)

Internal problem ID [8482]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 52 (b)
Date solved : Tuesday, September 30, 2025 at 05:38:00 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }-4 y&=x^{6} {\mathrm e}^{x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=y_{0} \\ \end{align*}

✗ Maple

ode:=x*diff(y(x),x)-4*y(x) = x^6*exp(x); 
ic:=[y(0) = y__0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=x*D[y[x],x]-4*y[x]==x^6*Exp[x]; 
ic={y[0]==y0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

{}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**6*exp(x) + x*Derivative(y(x), x) - 4*y(x),0) 
ics = {y(0): y__0} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Couldnt solve for initial conditions